In recent years, in achieving a microfabricated and highly-functional semiconductor device, the type of defects in a highly-integrated memory device has been particularly various among functional modules. In addition to foreign-substance defects such as a wiring short, disconnection, and interlayer disconnection defects due to foreign substances occurring in each process, a lot of systematic defects (parametric defects) such as a defective wiring pattern shape due to thickness variation in an in-plane wafer and variations in transistor operation have increasingly occurred (hereinafter, these defects are referred to as characteristic defects). Therefore, in order to quickly start up a yield, it is important to quantify a ratio of occurrences of the characteristic defects and foreign-substance defects of each process, and further, to specify the cause of the defects by investigating a manufacturing apparatus, chamber, and manufacturing condition for each cause of the defects and take an action for the cause of the defects.
In a memory device, as one of the defect analyzing methods, a fail-bit analyzing method has been conventionally widely used, in which a circuit is electrically judged as pass or failure for each cell which is a minimum unit for data reading/writing. An influential range of the failure cell differs depending on a size of the occurring foreign substance and a location of the occurrence such that the defect has occurred due to a short circuit by a word line and a data line or by a data line, a power supply line, and a word line. Therefore, in the fail-bit analyzing method, depending on the region of occurrence of such a defective cell, occurring defects are defined as a fail bit mode such as a single-bit defect, a pair-bit defect, and a word-line defect. In this manner, from a ratio of occurrence of the fail bit mode, it is possible to estimate in which layer, on which wiring, and with which degree of the size the foreign substance has occurred, and, as a method of quantifying the ratio of occurrence of the fail bit mode, the following method has been reported (Patent Document 1).
The defective ratio of each fail bit mode can be expressed by Expression (1) in a case of assumption of a Poisson model for yield prediction.
                                              ⁢                  [                      Expression            ⁢                                                  ⁢            1                    ]                                                                              [                                                                      Ac                                      FBM                    ⁢                                                                                  ⁢                    1                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    1                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    1                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    2                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    1                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    3                                                                              ⋮                                                              Ac                                      FBM                    ⁢                                                                                  ⁢                    1                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    n                                                                                                                        Ac                                      FBM                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    1                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    2                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    3                                                                              ⋮                                                              Ac                                      FBM                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    n                                                                                                                        Ac                                      FBM                    ⁢                                                                                  ⁢                    3                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    1                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    3                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    2                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    3                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    3                                                                              ⋮                                                              Ac                                      FBM                    ⁢                                                                                  ⁢                    3                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    n                                                                                                      ⋮                                            ⋮                                            ⋮                                            ⋮                                            ⋮                                                                                      Ac                                      FBM                    ⁢                                                                                  ⁢                    m                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    1                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    m                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    2                                                                                                Ac                                      FBM                    ⁢                                                                                  ⁢                    m                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    3                                                                              ⋮                                                              Ac                                      FBM                    ⁢                                                                                  ⁢                    m                    ⁢                                                                                  ⁢                    _                    ⁢                                                                                  ⁢                    Layer                    ⁢                                                                                  ⁢                    n                                                                                ]                ⁢                                                       [                                                                                          D                      ⁢                                                                                          ⁢                                              0                                                  Layer                          ⁢                                                                                                          ⁢                          1                                                                                                                                                                                D                      ⁢                                                                                          ⁢                                              0                                                  Layer                          ⁢                                                                                                          ⁢                          2                                                                                                                                                                                D                      ⁢                                                                                          ⁢                                              0                                                  Layer                          ⁢                                                                                                          ⁢                          3                                                                                                                                                          ⋮                                                                                                              D                      ⁢                                                                                          ⁢                                              0                                                  Layer                          ⁢                                                                                                          ⁢                          n                                                                                                                                ]                        =                          [                                                                                          -                                              ln                        ⁡                                                  (                                                      1                            -                                                          F                                                              FBM                                ⁢                                                                                                                                  ⁢                                1                                                                                                              )                                                                                                                                                                                -                                              ln                        ⁡                                                  (                                                      1                            -                                                          F                                                              FBM                                ⁢                                                                                                                                  ⁢                                2                                                                                                              )                                                                                                                                                                                -                                              ln                        ⁡                                                  (                                                      1                            -                                                          F                                                              FBM                                ⁢                                                                                                                                  ⁢                                3                                                                                                              )                                                                                                                                                          ⋮                                                                                                              -                                              ln                        ⁡                                                  (                                                      1                            -                                                          F                                                              FBM                                ⁢                                                                                                                                  ⁢                                m                                                                                                              )                                                                                                                                ]                                                          (        1        )            
Here, “D0Layern” represents the number of foreign substances of each process, “FFBMm” represents a defective ratio of each fail bit mode, and “AcFBMm—Layern” represents a critical area which is an integrated value of a foreign-substance sensitivity “θFBMm—Layern” of each process in each fail bit mode with a memory device area A. The foreign-substance sensitivity θFBMm—Layern of each fail bit mode is calculated from a foreign-substance sensitivity “θWiring combination—Layern” of each wiring combination. The foreign-substance sensitivity θWiring combination—Layern of each wiring combination can be calculated (by Expression (3)) as summation of products of a foreign-substance occurrence probability function “f(x)” indicating an occurrence probability of each size of the foreign substance expressed by Expression (2) with a critical probability distribution “g(x)Wiring combination—Layern” of each size of the foreign substance and each wiring combination calculated by a simulation for judging a critical foreign substance by virtually dropping the foreign substance onto a design layout of each process whose wiring names such as a power-supply line and a data line are previously defined.[Expression 2]f(x)=(n−1)×X0(n−1)×X−n  (2)
      [          Expression      ⁢                          ⁢      3        ]                                            θ                          Wiring              ⁢                                                          ⁢              combination_Layern                                =                                    ∑                              x                ⁢                                                                  ⁢                0                            ∞                        ⁢                                          f                ⁡                                  (                  x                  )                                            ×                                                g                  ⁡                                      (                    x                    )                                                                    Wiring                  ⁢                                                                          ⁢                  combination_Layern                                                                                          (          3          )                    
Here, “n” in Expression (2) represents a particle-size distribution parameter, and “X0” represents a minimum defect size. By finding a defective wiring combination, a resulting fail bit mode can be defined. Therefore, from the foreign-substance sensitivity θWiring combination—Layern of each process and each wiring combination, “θFBMm—Layern” for each process and for each fail bit mode is calculated by Expression (4).
      [          Expression      ⁢                          ⁢      4        ]                                            θ            FBMm_Layern                    =                                    ∑              1              N                        ⁢                          θ                              Wiring                ⁢                                                                  ⁢                combination_Layern                                                                          (          4          )                    
Here, “N” represents a total number of wiring combinations resulting in an arbitrary fail bit mode. The critical area AcFBMm—Layern calculated by multiplying this θFBMm—Layern by the memory device area and an actual defective ratio FFBMm of each fail bit mode are substituted into the yield-calculating Expression (1), and an inverse matrix is solved, so that the number of foreign substances of each process is calculated.